Zhong-Zhi Bai

TL;DR: This paper solves the boundary value problems of third‐order ordinary differential equations by sinc discretization and proves that the discrete solutions converge to the true solutions of the ODEs exponentially.

TL;DR: It is proved that the discrete solution resulting from the linear system converges exponentially to the true solution of the order‐reduced system of ODEs, and the eigenvalues of certain approximation to the preconditioned matrix are uniformly bounded within a rectangle on the complex plane independent of the size of the discretized linear system.

TL;DR: These modified incomplete Givens orthogonalization (MIGO) methods can preserve certain useful properties of the original matrix, and numerical results are used to verify the stability, the accuracy, and the efficiency of the MIGO methods employed to precondition the Krylov subspace iteration methods such as GMRES.

TL;DR: In this article, the convergence rate of the two-stage multisplitting method with one inner iteration is shown to be either faster or slower than that with many inner iterations.

TL;DR: This work proves local quadratic convergence of the inexact simplified Jacobi–Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration, which particularly leads to local cubic convergence when the relaxed correction equations is solved to a prescribed precision proportional to the norm of the current residual.